STATISTICS
, Thermodynamics Review
oth law : if system A is in equilibrium with system B and
system B is in
equilibrium with system C then A is in equilibrium
·
, ,
with C
.
1 law : U =
Qin + Won .
For anadiabatic process Q =
0 and the work done is path independent.
Q
·
2nd law : the entropy of an isolated system will either be constant or increase S =
T
·
3rd law : as T- O then So
·
The thermodynamic identity : U = Tds- PdV(+ MdN)
Enthalpy H U + PV
·
: =
Gibbs H-TS
free energy : G
·
= =
U-TS + PV
Helmholtz free
energy : f
U-TS
·
=
Introduction to Probability
Consider an experiment with r
mutually exclusive outcomes of X : (i = 1 2
. ...
r) We define p
.
,
as the probability of
outcome i.
&Pi = 1 >
-
probability of not obtaining s : is I-P. . The mean value of sis ( =
EP
Independent events :
if two events are independent then the probability that both occur is Pa
,
B
=
PAPB
Probability >
-
Statistical Physics
Microstate : a
complete description of the state of a system eg the energy that each atom has .
Macrostate : a description
of the overall state eg how many atoms have a particular energy
.
& total number of microstates of a system /number of accessible microstates
N!
The objects when order matters is n! out of N then P =
CN-ns !
number of ways of
arranging n or for
N 1
The objects out of N options when order does not matter is C =
arranging
=
number of ways of n
n! (N n) !
-
Eg . the number of ways of arranging 3 objects in 3 %= 6
Eg. the number of combinations of 3 objects chosen from 1 is = 4
for large n we can use Stirling's approximation : In (n ! ) =
n(n(n) -
n
To find the most probable macrostate : In 1 = In N ! - Inn ! -In (N -n) !
= NInN-N -nInn + n -
(N -
n)(n(N u) -
+ N -
n
=
NInN-nInn -
(N -n)(n(N -n)
=
din -Inn (n(N -n)
(n(N n) = N n 1 = n
=
= + 0
-
=
-
=
an H
Averaging postulate :
for a system in thermodynamic equilibrium all accessible microstates are equally probable
Statistical definition of entropy : S =
kind Entropy shows the direction of a spontaneous process -
disorder
, Thermodynamics Review
oth law : if system A is in equilibrium with system B and
system B is in
equilibrium with system C then A is in equilibrium
·
, ,
with C
.
1 law : U =
Qin + Won .
For anadiabatic process Q =
0 and the work done is path independent.
Q
·
2nd law : the entropy of an isolated system will either be constant or increase S =
T
·
3rd law : as T- O then So
·
The thermodynamic identity : U = Tds- PdV(+ MdN)
Enthalpy H U + PV
·
: =
Gibbs H-TS
free energy : G
·
= =
U-TS + PV
Helmholtz free
energy : f
U-TS
·
=
Introduction to Probability
Consider an experiment with r
mutually exclusive outcomes of X : (i = 1 2
. ...
r) We define p
.
,
as the probability of
outcome i.
&Pi = 1 >
-
probability of not obtaining s : is I-P. . The mean value of sis ( =
EP
Independent events :
if two events are independent then the probability that both occur is Pa
,
B
=
PAPB
Probability >
-
Statistical Physics
Microstate : a
complete description of the state of a system eg the energy that each atom has .
Macrostate : a description
of the overall state eg how many atoms have a particular energy
.
& total number of microstates of a system /number of accessible microstates
N!
The objects when order matters is n! out of N then P =
CN-ns !
number of ways of
arranging n or for
N 1
The objects out of N options when order does not matter is C =
arranging
=
number of ways of n
n! (N n) !
-
Eg . the number of ways of arranging 3 objects in 3 %= 6
Eg. the number of combinations of 3 objects chosen from 1 is = 4
for large n we can use Stirling's approximation : In (n ! ) =
n(n(n) -
n
To find the most probable macrostate : In 1 = In N ! - Inn ! -In (N -n) !
= NInN-N -nInn + n -
(N -
n)(n(N u) -
+ N -
n
=
NInN-nInn -
(N -n)(n(N -n)
=
din -Inn (n(N -n)
(n(N n) = N n 1 = n
=
= + 0
-
=
-
=
an H
Averaging postulate :
for a system in thermodynamic equilibrium all accessible microstates are equally probable
Statistical definition of entropy : S =
kind Entropy shows the direction of a spontaneous process -
disorder
